m³/hab.ano (vazão média)
6.11 A crise hídrica sob a ótica da dinâmica do poder
The results from test of the algorithms to detect and correct bias faults in temperature sensors are presented in Table 2. The instigated fault and the driving conditions (outdoor-air and return- air temperatures) during the test are shown on the left side of the table. On the right side of the table are the results of each stage of the SCC process. In the passive detection column, the type of passive test that was responsible for the detection of the fault (when applicable) is displayed. Two passive tests are used to detect a temperature sensor fault (see Fernandez et al. 2009). The “Temperature Sensor Passive Diagnostic Test” (Fernandez et al. 2009, Figure 5; see Appendix), abbreviated in the “Passive Detection” column of Table 2 as “Temp,” checks whether the mixed-air temperature is within the bounds of the return-air and the outdoor-air temperatures, because a failure to be within these bounds is physically impossible and indicates a sensor error. The second test, the “Minimum Occupied Position Passive Test” (Fernandez et al. 2009, Figure 6; see Appendix), checks whether the observed OAF at the minimum occupied position is close enough to the expected OAF at the minimum occupied position, based on response curve for the outdoor-air damper (like that shown in Figure 7) and accounting for the temperature sensor tolerances. This fault is abbreviated in the “Passive Detection” column of Table 2 as M.O.P.
Table 2: Results of tests for biased temperature sensors.
Test # Sensor and Severity Outdoor Air Temperature Return Air Temperature Passive Detction Proactive Diagnostics Fault Correction
Baseline None 39‐47°F 60‐79°F None None None
T‐1 TRA, ‐3°F 35‐45°F 70‐75°F
T‐2a TRA, ‐3°F 53‐58°F 68‐75°F M.O.P TMA +2.3°F, MA
T‐2b TRA, ‐3°F 53‐57°F 66‐77°F M.O.P TRA ‐2.3°F, RA
T‐3 TRA, +3°F 50‐60°F 60‐80°F T‐4 TRA, +5°F 45‐50°F 75‐80°F
T‐5a TRA, ‐5°F 53‐57°F 70‐72°F M.O.P TRA ‐4.2°F, RA
T‐5b TRA, ‐5°F 49‐51°F 70‐75°F M.O.P TMA +3.8°F, MA
T‐6 TRA, ‐8°F 53‐59°F 67‐77°F Temp TRA ‐7.5°F, RA
T‐7 TRA, +8°F 49‐51°F 64‐66°F M.O.P TRA +9.0°F, RA
T‐8a TOA, +8°F 56‐58°F 70‐74°F T‐8b TOA, +8°F 45‐53°F 70‐75°F T‐9 TOA, ‐8°F 56‐58°F 70‐72°F
In the “Proactive Diagnostics” column of Table 2, the temperature sensor that was identified as being at fault (if a fault was detected passively) is identified. In the “Fault Correction” column of Table 2, the magnitude of the constant bias correction to the sensor identified as faulty is displayed. In each of the last three columns, green shading is used to indicate stages of each test that produced the desired result and red shading is used to indicate stages that produced incorrect results. The incorrect result could be caused by either a lack of robustness in the SCC algorithms, or, in the case of some undetected faults, a fault severity below the limits for
The first test performed was a baseline test in which no faults were present. It was performed to verify that no faults would be detected when none were instigated. This test was run for 16 hours. Despite some sharp oscillations in the return-air temperature, no faults were detected during the test. Figure 8 shows the mixing-box temperatures over the duration of the test. Solid lines in this plot identify the actual temperatures measured by the sensors, and dashed lines identify the virtual temperatures that the SCC program acts upon. In this case, because no faults were instigated, the two lines for each sensor overlap perfectly in Figure 8. During the baseline test, the mixed-air temperature always stayed safely within the bounds of the outdoor- and return-air temperatures, creating no risk of a fault being detected in the passive test. Figure 9 shows the virtual OAF, the measured OAF, and the damper command versus time for the baseline test. The damper command (black line) was held constant at 35 because at the minimum occupied position. The red lines represent the limits for detection of a fault for detection of a fault. These limits are based on the tolerances set for the temperature sensors, which are propagated through the OAF calculation (see Fernandez et al. 2009, Section 2.5), and thus are functions of the difference between the outdoor-air and return-air temperatures. The virtual OAF fluctuates during the test but always remains within the bounds for its expected value. The fluctuation is attributable to a delayed transient response of the OAF to changes in the driving conditions. A hypothesis potentially explaining this observed behavior of the OAF is that the measured transient response is affected by the use of two different types of
temperature sensors (the averaging sensor for the mixed-air temperature, and the single-point probe-type sensors elsewhere), which respond at different rates. The averaging sensor may respond to changes in air temperature faster than the probe-type sensor, leading to fluctuations in the calculated OAF as driving conditions change. This hypothesis requires testing in future work to better understand the observed behavior.
Figure 10 shows the progression of fault detection, diagnosis, and correction for T- 7 in which a return-air temperature sensor bias fault of +8F is present, leading to successful correction of the fault. Vertical lines labeled with numbers above the plot identify key events in the process. As done in Figure 8, the damper position is shown for comparison to the temperature
responses. At the onset of the test, the system operated with all sensors reading the correct values, and with no bias instigated. The damper system was in the minimum occupied position, with a damper command signal of 35. At point 1 (vertical line), an 8°F positive bias was
instigated in the return-air sensor (i.e., the virtual return-air sensor). At this point, the virtual return-air temperature (dashed red line) increase 8°F above the measured return-air reading because it now has a fault. At point 2, a fault is detected in the minimum occupied position
Figure 8: Baseline test – temperatures.
Figure 9: Baseline test - OAF and damper command.
passive test because the virtual OAF is 53%, which is greater than upper limit for fault detection of 43% at that time. The system was running in automatic mode, so immediately following detection of a fault, the proactive diagnostic test began. The OA damper was commanded to 0 (completely closed outdoor-air damper), the program waited until steady state was reached and then determined that the mixed- and return-air temperatures were not close enough to be considered equal. At this point (point 3), the damper signal was commanded to 100 (fully open outdoor-air damper) and when steady state was reached, the program determined that the outdoor-air and mixed-air temperatures were close enough to be considered equal. This led to
the conclusion that the mixed-air sensor was faulty (i.e., the fault was isolated to an individual sensor). The, at point 4, the fault characterization and correction processes began. The
damper was commanded to 0, and steady state was reached at point 5. The SCC process then recorded the differences between the mixed- and return-air virtual temperature measurements to determine if the bias was approximately constant over time, which it was. The SCC program then averaged the measured differences in temperature between the (virtual) mixed- and return- air sensors, and used this difference to apply a correction to (i.e., effectively recalibrate) the (virtual) return-air sensor. The SCC program determined the bias to be 8.98°F, nearly 1°F above the actual 8°F bias fault that was implemented. At point 6, the fault correction ended, the corrected bias was applied to the virtual return-air temperature, and the system returned to normal operation at the minimum occupied damper position. The entire process took approximately 1 hour.
Figure 10: Test T-7-- detection, diagnosis and correction of a biased return-air temperature sensor.
Tests T-1 and T-3 featured biases of -3°F and +3°F in the return-air (virtual) temperature sensor, with 2°F tolerances applied to all temperature sensors. The results of these two tests clearly showed that a bias severity of 3°F was too small to detect with the algorithms at the current tolerance magnitude of 2°F. Figure 11 shows the mixing box temperatures during Test T-1. The decrease in the virtual return-air temperature caused by instigation of the bias fault was not sufficient to decrease it below the virtual mixed-air temperature that a temperature- sensor fault was detected by the passive test.
Driving conditions have an important effect on the minimum severity detectable by the passive test for temperature-sensor faults. During the baseline test with no fault present, the outdoor-air and return-air temperatures were only about 9°F apart at the beginning of the test (see Figure 8). Consequently, at a damper signal of 35 for the minimum occupied position, only about a 2°F difference existed between the return-air and the mixed-air temperatures. Under these
return-air temperature below the virtual mixed-air temperature; however, accounting for
tolerances, this would not have been sufficient for detection of the fault. When this observation is compared to Figure 11, where the virtual return-air temperature remains 3 to 5°F above the mixed-air temperature, the large impact that actual ambient conditions can have on the limits for fault detection is evident. This effect is more pronounced for the passive test for detection of a temperature sensor fault. The minimum occupied position passive test, on the other hand, sets limits for fault detection that are a function of the outdoor- and return- air temperatures, so the driving conditions are less important, but as will be shown later, they still play an important role in determining the severity of a fault that can be detected.
Figure 11: Test T-1 -- Mixing Box Temperatures
Figure 12 shows the actual measured OAF and the virtual OAF, as well as the OAF limits for fault detection during Test T-1. The virtual OAF remains almost steady at a level 5% above the lower limit for fault detection (line labeled OAF-). Unlike during the baseline test, the driving conditions were quite steady during Test T-1, which may have contributed to some degree to the virtual OAF never approaching the fault detection limits.
To investigate the ability of the algorithms to detect and correct the same fault under tighter temperature tolerances, the test for a -3°F bias in the return-air temperature sensor was run but with +/-1°F tolerances in for all temperature sensors (rather than +/-2°F tolerances). The first time this test was run (Test T-2a), the fault was passively detected in the minimum occupied position test, with a virtual OAF of 17% and the lower limit for fault detection at 19%. An incorrect isolation of the fault to the MA temperature sensor was made, however. Recall from the “Temperature and Damper Proactive Diagnostics” test process (Fernandez et al. 2009, Figures 3; see Appendix) that temperature sensor faults are isolated by comparing the mixed-air temperature to the return-air temperature with the OA damper completely closed, then
comparing the mixed-air temperature to the outdoor-air temperature with the OA damper completely open. If the dampers are operating properly, four outcomes are possible from this test:
Figure 12: Test T-1 - OAF and Dampers
1) If the MA and the RA temperatures are equal within tolerances, and the MA and the OA temperatures are not equal within tolerances, the fault is isolated to the outdoor-air sensor.
2) If the MA and RA temperatures are not equal within tolerances, and the MA and the OA temperatures are equal within tolerances, the fault is isolated to the return-air sensor. 3) If the MA and the RA temperatures are not equal within tolerances, and the MA and the
OA temperatures are not equal within tolerances, the fault is isolated to the mixed-air sensor.
4) If the MA and the RA temperatures are equal within tolerances, and the MA and the OA temperatures are equal within tolerances, no temperature sensors are determined to be faulty, and instead the damper position is determined to be set incorrectly, according to the desired OAF.
The mixed-air and return-air temperatures were determined to not be equal when the test apparatus OA damper was fully closed. It was also determined that the mixed-air and outdoor- air temperatures were not equal when the outdoor-air damper was fully open (the mixed-air temperature was 2.2 degrees higher than the outdoor-air temperature in this case). The differences were caused partly by the temperature tolerances being as small as they were. Another cause for the discrepancy between the mixed- and outdoor-air temperatures when they should have been approximately equal can be inferred from Figure 7. Leakage when dampers are fully closed resulted in a minimum OAF of 10% at all times, including during the proactive diagnostic tests, which are designed to isolate the flows of outdoor and return air. If the outdoor-air and return-air temperature difference is 20°F during the proactive diagnostics, the 10% OAF associated with leakage when the outdoor-air damper is fully closed will cause a 2°F difference in these temperatures. Because the return-air damper also leaks when fully closed, the inverse is also true, so the maximum achievable OAF is around 90%. Damper leakage is an important factor that is not handled by the existing algorithms, but which needs to be addressed
in future versions to avoid incorrect diagnoses and attempted fault corrections. In the case of Test T-2a, the algorithms went on to incorrectly implement a “correct” the mixed-air sensor by attributing a +2.3°F bias correction to the mixed-air temperature sensor (see Table 2). This same test was rerun with slightly different temperatures as Test T-2b. In this case, the proactive diagnostics reached the correct conclusion, and the return-air sensor was subsequently
corrected by 2.3°F.
The same problem that plagued Test T-2a also led to the incorrect diagnosis of a mixed-air temperature sensor fault in Test T-5b. Although there were 2°F tolerances applied to this test, the same incorrect decision was made that the mixed-air and outdoor-air temperatures were not close enough to being equal during the proactive diagnostics with a fully open outdoor-air damper. In this case, the problem was caused by the difference between the outdoor- and return-air temperatures being even greater than in Test T-2a. The solution to this problem should be the same, however -- the diagnostics need to account for normal damper leakage. The return-air temperature sensor tests seemed to indicate that with 2°F temperature sensor tolerances, the threshold for detection of a temperature sensor bias fault is about 5°F. One test was performed on the mixed-air sensor at a high fault severity level of 8°F, and the fault was detected and corrected. For the outdoor-air temperature sensor, however, even at the 8°F level of fault severity, the fault remained undetected for both a positive and negative instigated
biases. Understanding the reason for the lack of detection requires examining details of the rules for fault detection.
The temperature sensor passive fault detection test itself is somewhat limited. It requires the right set of conditions such that an instigated temperature-sensor bias will produce a set of virtual temperatures for which the mixed-air temperature is outside the range between the outdoor-air and return-air temperatures (and by enough to conclusively determine that a fault exists, considering sensor tolerances). Indeed, the passive temperature sensor test was only versatile enough to correctly detect one fault during the 13 temperature sensor bias tests that were performed. The passive test for the minimum occupied position, on the other hand, is much more versatile, because it is a relative test. It only requires that the virtual OAF differ substantially from the expected value of the OAF. This test, however, has its own limitations, especially in detecting outdoor-air sensor faults. Outdoor-air sensor biases cause a
proportionately smaller change in the OAF, compared to biases in the mixed-air and the return- air sensors. The outdoor-air temperature appears only in the denominator of the OAF equation. It is, therefore, difficult to distinguish a deviation from the normal OAF that is caused by an outdoor-air bias from one that is caused by normal variations. Figure 13 through Figure 18 show the intrinsic level of fault severity necessary to detect either positive or negative bias faults in each of the three sensors. The term ‘intrinsic level’ means (in this case) “in the absence of any transient behavior, sensor noise, or other factors that might influence the ability to detect a fault.” These plots are valid for a return-air temperature of 70°F (approximate room
temperature), an actual OAF of 30%, and +/-2°F tolerances for all sensors. The darker shading in each plot identifies regions of intrinsic fault detection ability. Figure 17 and show that for detection of bias faults in mixed-air temperature sensors, the threshold of fault severity for detection is between 3 and 5°F, the precise value of the threshold depending on the
temperature and the sign of the bias. For return-air temperature sensors, the threshold is between 4 and 6°F for most conditions, as shown in Figure 15 and Figure 16. For outdoor-air sensors, however, the threshold is generally greater than 8°F, and more typically in the range of 12 to 15°F (see Figure 13 and Figure 14). This represents a limitation of the fault detection algorithms for which there may be no easy solution without changing the underlying method.
Figure 13: Intrinsic level of fault severity necessary to detect positive bias faults in OA temperature sensors using the minimum occupied position passive test.
Figure 14: Intrinsic level of fault severity necessary to detect negative bias faults in OA temperature sensors using the minimum occupied position passive test.
Figure 15: Intrinsic level of fault severity necessary to detect positive bias faults in RA temperature sensors using the minimum occupied position passive test.
Figure 16: Intrinsic level of fault severity necessary to detect negative bias faults in RA temperature sensors using the minimum occupied position passive test.
Figure 17: Intrinsic level of fault severity necessary to detect positive bias faults in MA temperature sensors using the minimum occupied position passive test.
Figure 18: Intrinsic level of fault severity necessary to detect negative bias faults in MA temperature sensors using the minimum occupied position passive test.